Simplify the following expression: $ r = \dfrac{-10}{7} - \dfrac{-10n - 8}{-10n + 2} $
Explanation: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-10n + 2}{-10n + 2}$ $ \dfrac{-10}{7} \times \dfrac{-10n + 2}{-10n + 2} = \dfrac{100n - 20}{-70n + 14} $ Multiply the second expression by $\dfrac{7}{7}$ $ \dfrac{-10n - 8}{-10n + 2} \times \dfrac{7}{7} = \dfrac{-70n - 56}{-70n + 14} $ Therefore $ r = \dfrac{100n - 20}{-70n + 14} - \dfrac{-70n - 56}{-70n + 14} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{100n - 20 - (-70n - 56) }{-70n + 14} $ Distribute the negative sign: $r = \dfrac{100n - 20 + 70n + 56}{-70n + 14}$ $r = \dfrac{170n + 36}{-70n + 14}$ Simplify the expression by dividing the numerator and denominator by -2: $r = \dfrac{-85n - 18}{35n - 7}$